Problem $1$: A beam section has to be reinforced using $20$M$,25$ M and $30$ M bars.

Suggest the suitable combinations using an even number of bars if the required area of steel is:

a$)1650m{m}^2$

b$)3300m{m}^2$

c$)4700m{m}^2$

d$)5500m{m}^2$

Problem $2$:

Consider a simply supported unreinforced beam of square cross$-$section $(\{$:$150150m{m}^2)$ spanning

over $900$ mm $.$ The beam was loaded by a point load at mid$-$span and failed when the load reached

$7\mathrm{.}5$ kN $.$ The concrete used is of normal density of $2300k\frac{g}{m^3}.$ Determine the modulus of rupture for

this beam under the following two assumptions.

a$)$ Ignoring the self$-$weight

b$)$ Including the self$-$weight.

Compare the results obtained in a$)$ and b$)$ with the estimation given by the CSA A$23\mathrm{.}3$ standard. Use

$f_c^{\text{'}}=25$MPa.

Problem $3$:

Following the recommendations of the NBC $2020,$ determine the specified uniformly distributed live

load:

a$)$ The second floor of an office building.

b$)$ A floor in a parking garage of passenger cars.

c$)$ A college library $($at maximum load$).$